In this video I go over a pretty useful example on solving integrals by the method of integration by parts. The example I cover is the integral of the function x·sin(x) and show how to apply the integration by parts method as well as the simplified version using the u, du, v, dv method. I go into great detail in this example to make sure to illustrate the method of integration by parts as best as I can so make sure to watch this video!
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Example:
Solution:
Integration by Parts Formula:
Can double check our answer by differentiating:
Solution using the second formula I covered in my last video (which uses the Substitution Rule)
Important Note: Our aim in using integration by parts is to obtain a simpler integral than the one we started off with:
But if we had chosen:
Now we have ended up with a more difficult integral!
Thus in general, when deciding on a choice for u and dv, we usually try to choose u = f(x) to be a function that becomes simpler when differentiated (or at least not more complicated) as long as dv = g'(x)dx can be readily integrated to give v.
